The reviewer had a few more points than just that, such as how the author not only fails to point out that luck is correlated with success, but contradicts himself.

Even in that statement you quoted out of context, the reviewer is referring to how we all have the same amount of luck, so luck alone shouldn't be the basis for a progressive tax.

Now, there are good reasons for a progressive tax, but the reviewer is saying it doesn't justify ignoring illogical arguments in the book. Just because the conclusion is proven right somewhere else doesn't mean that all arguments for it are valid.